1. Field of the Invention
The present invention relates to architectural graphics, and more particularly to a computerized process for determining the best-fitting materials for constructing architectural surfaces, especially curved surfaces.
2. Description of the Related Art
In three-dimensional (3D) modeling, it is often necessary to approximate freeform surfaces with a combination of tiles of regular shapes, such as rectangles, triangles, ovals, and various polygons. When designing, architects often need the freedom to create complexly curved surfaces for structures such as walls and rooftops, without being constrained by regular geometries. Such freeform curves, however, are difficult to realize during construction, because building materials are typically supplied in pieces that have planar surfaces, or curved surfaces that conform to regular cylindrical, spherical, or conical geometries.
Although it is possible to approximate a freeform curve with such geometries, the approximation must be done iteratively through numerical optimization, beginning with an initial best guess, and searching for better-fitting configurations by trial and error.
Currently, one known approach to solving this problem is global optimization, in which a freeform shape is distorted to match a regular shape so that it is more constructible. Another approach is local optimization, which attempts to fit classes of shapes to specific surfaces. These approaches are computationally slow, and tend to sacrifice too much accuracy in arriving at an approximate solution. When applied to very complex curved surfaces, such as those shown in FIG. 1, the shape-fitting problem can be extremely time-consuming and the errors introduced by global and local optimization solutions may not be satisfactory to the architect.
What is needed is a more accurate and computationally efficient process for determining the best-fitting construction materials for realizing freeform curves.